In this paper, we have explored in greater detail some of the ideas
presented in [1]} for obtaining “\({\cal N}=0\)  supergravity”
(i.e. the low-energy limit of the bosonic string) as a convolutional
double copy of Yang-Mill squared. A crucial aspect of the construction in
[1]} is the inclusion of the ghosts and antighosts of a BRST
description, in order to capture fully the degrees of freedom of
the theory. Accordingly, our discussion has been centred around the
BRST description of the theory and its gauge invariances, with an
emphasis on the anti-BRST as well as the BRST symmetries of the system.
